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A273801 Numbers n for which n = (x - phi(x)) * (y - phi(y)), where n = x + y and x - phi(x) is the Euler cototient function of x.

%I A273801 #12 Sep 06 2017 02:54:44
%S A273801 16,24,32,48,56,72,80,96,120,128,152,168,176,192,216,240,248,272,288,
%T A273801 296,320,336,360,392,408,416,432,440,456,512,528,552,560,600,608,632,
%U A273801 656,672,696,720,728,768,776,792,800,848,896,912,920,936,960,968,1008,1032
%N A273801 Numbers n for which n = (x - phi(x)) * (y - phi(y)), where n = x + y and x - phi(x) is the Euler cototient function of x.
%H A273801 Paolo P. Lava, <a href="/A273801/b273801.txt">Table of n, a(n) for n = 1..200</a>
%F A273801 a(n) = 4*(prime(n+1) + 1). - _Paolo P. Lava_, Sep 06 2017
%e A273801 16 = 4 + 12 = (4 - phi(4)) * (12 - phi(12)) = 2 * 8 = 16 and also
%e A273801 16 = 8 + 8 = (8 - phi(8)) * (8 - phi(8)) = 4 * 4 = 16;
%e A273801 24 = 4 + 20 = (4 - phi(4)) * (20 - phi(20)) = 2 * 12 = 24.
%p A273801 with(numtheory): P:=proc(q) local a,b,k,n; for n from 1 to q do
%p A273801 for k from 1 to trunc(n/2) do if (k-phi(k))*(n-k-phi(n-k))=n then print(n); break; fi;
%p A273801 od; od; end: P(10^9);
%t A273801 Select[Range@ 1032, Function[n, Length@ Select[Times @@ Map[(# - EulerPhi@ #) &, {#, n - #}] & /@ Range[0, Floor[n/2]], # == n &] > 0]] (* _Michael De Vlieger_, Jun 01 2016 *)
%Y A273801 Cf. A051953, A273800.
%K A273801 nonn
%O A273801 1,1
%A A273801 _Paolo P. Lava_, May 31 2016